Problem #PRU-100230

Problems Algebra Graphs and locus of points on the Cartesian plane

Problem

There are 9 cities named City 1, City 2, City 3, …, and City 9 in a country named The Country of the Nine Cities. Two cities are connected by a road only if the sum of the numbers made up by their names is divisible by 3. Can our travelling architect reach City 9 by starting his journey from City 1 and travelling along those roads?